They've always been there occasionally, but now she's 7 months old and we're just beginning to introduce her to food (not that she's particularly interested just yet), this question has become a regular one. My answer can't be given in just a word, though.
Firstly, being vegan is a life choice, not just a food choice. It means to abstain from willfully and unnecessarily causing harm to other sentient beings - and that includes not just eating them, but also wearing their skins or furs, using products that were tested on them, or exploiting them in the many ways humans have invented. But, let's keep things simple here and stick to the food, since that is what most people are thinking of when they ask the question.
A few thoughts on this.
I want her to be healthy.
I will do the best by her that I know how. This includes, but is not limited to, giving her the best nutrition to thrive. Why would I deliberately give her food that will, if not harm her, then at least be a burden on her system? Why not give her only what's good for her? So no, I won't give her animal flesh or secretions.
I want her to learn compassion.
I want her to grow up asking what effects her actions are having on others. Human and non-human. She'll learn that kicking the dog is not kind. She'll learn that hitting another child is not okay. And she'll know from a young age that eating parts of other beings' bodies means that they have to die, and because we don't need to eat those body parts to survive, that is not a compassionate thing to do. When she's old enough to handle the truth, I will show her where meat comes from. We'll go to the city farms and pet the animals, and she'll see what gentle, sweet creatures they are.
I don't want to lie to her.
Like the little boy's mother in this video - I have such respect for her! - I will be honest with my child. I'll be honest about Santa Claus, I'll be honest about the Tooth Fairy, and I'll be honest about her food.
I want her to think for herself.
This applies to everything. Obviously as a small baby, I make choices for her. I make them to the best of my ability in her best interests. But ultimately, I can't raise her to be a vegan any more than I can raise her to be a Christian - I am both, with all my heart, and when she is young I will make choices for her along those lines; she'll grow up in that environment, see my example, learn my reasons... but I cannot make her life choices for her. When she is able to, she will have to make a proactive choice and I can only hope (and pray!) that what I have shown her and taught her will help her make those choices. But I can't and wouldn't force her!
It simply is the right thing.
I could go into so much detail about why living vegan is simply the morally right thing to do (quite apart from health wise...) - now, I'm not going to lie, living vegan sometimes means you miss out on (nonvegan) birthday cake, or (nonvegan) ice cream, or other things we think of as indispensable in a childhood. But is my child's questionable, short-term culinary pleasure worth the suffering behind it? When there is absolutely no nutritional need, and if anything, those things I mentioned are health liabilities anyway - simply for the fleeting gratification of a desire? As I see it, she may want ice cream but she hasn't understood what's behind it - the animal bred to give unnatural amounts of milk, existing its miserable life long in a tiny cage, artificially impregnated every year so that the milk won't stop but her calf, as soon as it's born, taken away (to be killed if male, to be subjected to the same fate if female), discarded after a few years when the milk no longer flows so freely; if my girl knew all this, she would not want the ice cream. But that kind of wider perspective comes with maturity, a little child doesn't have it - which is why I make that choice for her for now.
I will make other choices for her to do the right thing when she doesn't know yet. I will keep her away from harm. I will stop her harming others. It simply is the right thing to do.
Thank goodness for the support I have.
I'm grateful that I not only have a husband who, though not actually (fully) vegan himself, doesn't just "let me" bring up baby along these lines but actively thinks this is what we should do. My in-laws aren't vegans but I am beyond blessed with them: I feel completely respected by them and I trust that they will go along with the way my husband and I wish to raise our child - grandparents like that are the best! They are supportive, not undermining. When our daughter is with them I do believe that, if I make sure they understand what we're looking to instill in her, will respect those boundaries. That is a huge blessing and not one I take for granted... my family is far away but if my parents were still around - particularly my father's side - I have no doubt they would continually undermine us and seek to sneak "treats" behind our backs. It's wonderful to not have to deal with that.